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        riddles >> putnam exam (pure math) >> dimension of subspaces
        
(Message started by: Samantha on May 18^th, 2004, 5:52am)

Title: dimension of subspaces
Post by Samantha on May 18^th, 2004, 5:52am

Find the dimension of each of the following subspaces

a) W = {(x,y,z)|2x-y+z=0} in R3

b)The subspace of R4 consisting of all the vectors orthogonal to the vector a= (5,1,2,-3)

c) The subspace of R3 spanned by the vectors (1,-2,2),
(6,-1,5) and (4,3,1)

Title: Re: dimension of subspaces
Post by towr on May 18^th, 2004, 8:30am

::[hide]
a) two degrees of freedom, so D=2
b) only one direction is set, it takes 4 to span up the space, so D=3
c) linearly independant span set of size 3, so D=3
[/hide]::

Title: Re: dimension of subspaces
Post by Samantha on May 19^th, 2004, 6:00am

thanx!!! could you plz explain it in more detail...i'm confused as to why it is so